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To be sure. But it is useful in this particular case, so why wouldn't we use it? Similarly, you can write every multiplication or natural numbers as a summation, but we don't because multiplication notation adequately handles the case where the term of summation doesn't change and is simpler to reason about. The motivation for summation is that sometimes we want to add up things where multiplication notation fails. Similarly, the motivation for factoring is that sometimes we run into an equation that we can't intuitively reason about. His explanation would be more persuasive to me with an example where simple inspection fails.

If the target audience for the article is people who understand factoring and are amused by thinking about it in different ways (the bit about systemic error was new to me and intriguing!), then I think it succeeds. If the target audience for the article is people who don't yet understand how to factor, but do understand why to factor, then I think it sort-of succeeds. There are probably people (the author is certainly one?) for whom his explanation will seem intuitive and compelling. If the target audience is people who neither know how to factor or why, then I think it's more problematic.

It's symptomatic of a rush to abstract and generalize that often leaves students wondering why the abstractions are more valuable than more intuitive reasoning. An example that requires factoring would speak to that motivation a bit better, I suspect.



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